Inverse spectral problem for analytic $(Z/2Z)^n$-symmetric domains in $R^n$

Hamid Hezari; Steve Zelditch

Inverse spectral problem for analytic $(Z/2Z)^n$-symmetric domains in $R^n$

Analysis of PDEs 2010-07-13 v3 Spectral Theory

Authors: Hamid Hezari , Steve Zelditch

Abstract

In this paper we show that bounded analytic domains in $\R^n$ with mirror symmetries across all coordinate axes are spectrally determined among other such domains. Our approach builds on finding concrete formulas for the wave invariants at a bouncing ball orbit. The wave invariants are calculated from a stationary phase expansion applied to a well-constructed microlocal parametrix for the trace of the resolvent.

Keywords

inverse spectral problem analytic domains mirror symmetries wave invariants bouncing ball orbit stationary phase microlocal parametrix

Cite

@article{arxiv.0902.1373,
  title  = {Inverse spectral problem for analytic $(Z/2Z)^n$-symmetric domains in $R^n$},
  author = {Hamid Hezari and Steve Zelditch},
  journal= {arXiv preprint arXiv:0902.1373},
  year   = {2010}
}

Comments

29 pages; some typos corrected and references added

Inverse spectral problem for analytic $(Z/2Z)^n$-symmetric domains in $R^n$

Abstract

Keywords

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